Spatial Modeling in Public Health: A Review of Geographically Weighted Poisson Regression (GWPR) Applications

Authors

DOI:

https://doi.org/10.32493/sm.v8i1.54205

Keywords:

GWPR, Poisson, Public Health, Review

Abstract

Geographically Weighted Poisson Regression (GWPR) is an important approach in analyzing spatial count data, especially in the field of public health. However, its application in Indonesia still has various methodological weaknesses. This study aims to critically review the suitability and application of the GWPR model, as well as analyze aspects of statistical assumptions, weighting function selection, model evaluation, and methodological innovation. This study uses an article review approach of 10 research articles that apply GWPR in public health. The review results show that most studies have not explicitly articulated research gaps and novelty, and have ignored crucial offset variables in count data. Spatial heterogeneity testing is often performed incorrectly using the BP test instead of visual exploration through thematic maps. The selection of weighting functions and bandwidths is often not based on objective evaluation. Additionally, many studies have not conducted multicollinearity checks and tests of the assumption of equidispersion, which directly impact model validity. Descriptive analysis and visualization of local parameters through maps remain limited, hindering contextual interpretation. Finally, some studies fail to include model goodness-of-fit evaluations such as AIC or pseudo-R², making it impossible to demonstrate the superiority of GWPR over global models objectively. These findings underscore the importance of upholding statistical validation principles and methodological transparency in GWPR modeling to produce accurate and relevant spatial analyses for regional policy-making.

References

1. Karima N Al, Suyitno S, Hayati MN. Analisis Faktor-Faktor yang Mempengaruhi Jumlah Kasus Tuberkulosis di Indonesia Menggunakan Model Geographically Weighted Poisson Regression. Eksponensial. 2021;12(1):7.

2. Sintia I, Suyitno S, Hayati MN. Geographically Weighted Poisson Regression Model with Adaptive Bisquare Weighting Function (Case study: data on number of leprosy cases in Indonesia 2020). Jurnal Matematika, Statistika dan Komputasi. 2022;19(1):124–45.

3. Nakaya T, Fotheringham AS, Brunsdon C, Charlton M. Geographically weighted Poisson regression for disease association mapping. Stat Med. 2005 Sep 15;24(17):2695–717.

4. Setyawan Y, Suryowati K, Octaviana D. Applying negative binomial regression analysis to overcome the overdispersion of Poisson regression model for malnutrition cases in Indonesia. Bulletin of Applied Mathematics and Mathematics Education. 2022;2(2):87–96.

5. Saraiva EF, Vigas VP, Flesch MV, Gannon M, de Bragança Pereira CA. Modeling Overdispersed Dengue Data via Poisson Inverse Gaussian Regression Model: A Case Study in the City of Campo Grande, MS, Brazil. Entropy. 2022;24(9).

6. Picioroaga II, Tudose AM, Sidea DO, Bulac C. Supply Restoration in Active Distribution Networks Based on Soft Open Points with Embedded DC Microgrids. Mathematics. 2022 Jan 11;10(2):211.

7. Faroughi P, Li S, Ren J. The Applications of Generalized Poisson Regression Models to Insurance Claim Data. Risks. 2023;11(12):1–17.

8. Nasution AR, Sadik K, Rizki A. Perbandingan Kinerja Regresi Conway-Maxwell-Poisson dan Poisson-Tweedie dalam Mengatasi Overdispersi Melalui Data Simulasi. Xplore: Journal of Statistics. 2022;11(3):215–25.

9. Rana S, Al Mamun ASM, Rahman FA, Elgohari H. Outliers as a Source of Overdispersion in Poisson Regression Modelling: Evidence from Simulation and Real Data. International Journal of Statistical Sciences. 2023;23(2):31–7.

10. Azevedo AM, Silva ÍJ, Nery MC, Rocha HP, Santana RA. Counting models for overdispersed data: A review with application to tuberculosis data. Brazilian Journal of Biometrics. 2023;41(3):274–86.

11. Aswi A, Astuti SA, Sudarmin S. Evaluating the Performance of Zero-Inflated and Hurdle Poisson Models for Modeling Overdispersion in Count Data. Inferensi. 2022;5(1):17.

12. Zeleke AJ, Miglio R, Palumbo P, Tubertini P, Chiari L. Spatiotemporal heterogeneity of SARS-CoV-2 diffusion at the city level using geographically weighted Poisson regression model: The case of Bologna, Italy. Geospat Health. 2022;17(2).

13. Martafiyah, S., Supriadi, C., & Saifudin T. No Title. Modeling the maternal mortality rate in Indonesia using geographically weighted Poisson Regression approach. 2023;AIP Conf.

14. Yuliana A, Fauzan A. Spatial Modeling of Maternal Health: Geographically Weighted Poisson Regression on Maternal Mortality Factors. Barekeng. 2025;19(1):557–70.

15. Oshan, T. M., Li, Z., Kang, W., Wolf, L. J., & Fotheringham AS. Issue Information. A practical guide to multiscale geographically weighted regression. 2021;53(4):529–550.

16. Adeniran AO, Tayo-Ladega OT. Understanding Literature Review as A Research Method. American International Journal of Humanities, Arts and Social Sciences. 2024 Dec 30;26–35.

17. Snyder H. Literature review as a research methodology: An overview and guidelines. J Bus Res. 2019 Nov;104:333–9.

18. Farrukh A, Sajjad A. A Critical Review of Literature Review Methodologies. In 2023. p. 103–23.

19. Goldenfein J, Griffin D. Google Scholar – Platforming the scholarly economy. Internet Policy Review. 2022 Sep 29;11(3).

20. Martín-Martín A, Thelwall M, Orduna-Malea E, Delgado López-Cózar E. Google Scholar, Microsoft Academic, Scopus, Dimensions, Web of Science, and OpenCitations’ COCI: a multidisciplinary comparison of coverage via citations. Scientometrics. 2021 Jan 21;126(1):871–906.

21. Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, et al. Cochrane Handbook for Systematic Reviews of Interventions. Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, et al., editors. Wiley; 2019.

22. Agresti A. Statistical Methods for the Social Sciences. 5th ed. London: Pearson; 2021.

23. Hilbe JM. Modeling Count Data. Cambridge University Press; 2014.

24. Kutner MH, Nachtsheim CJ, Neter J. Applied Linear Regression Models. 4th ed. New York: McGraw-Hill Education; 2016.

25. James G, Witten D, Hastie T, Tibshirani R. An Introduction to Statistical Learning. New York, NY: Springer US; 2021.

26. Fotheringham AS, Brunsdon C, Charlton M. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley; 2002.

27. Brunsdon C, Fotheringham AS, Charlton ME. Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geogr Anal. 1996 Oct 3;28(4):281–98.

28. Aulele SN, Lewaherilla N, Matdoan MY. Pendekatan Geographically Weighted Poisson Regression dengan Pembobot Fungsi Kernel Gauss untuk Menganalisis Jumlah Kematian Bayi di Provinsi Maluku. Jurnal Aplikasi Statistika & Komputasi Statistik. 2022 Dec 30;14(2):67–80.

29. Wati F, Suyitno S, Hayati MN. Pencegahan Penyakit Kusta di Lingkungan Hutan Tropis Lembab Kalimantan Melalui Pemodelan Geographically Weighted Poisson Regression. EKSPONENSIAL. 2021 Jun 21;12(1):27.

30. Yuliana A, Fauzan A. Spatial Modeling of Maternal Health: Geographically Weighted Poisson Regression on Maternal Mortality Factors. BAREKENG: Jurnal Ilmu Matematika dan Terapan. 2025 Jan 13;19(1):557–70.

31. Sabtika W, Prahutama A, Yasin H. Pemodelan Geographically Weighted Generalized Poisson Regression (GWGPR) pada Kasus Kematian Ibu Nifas di Jawa Tengah. Jurnal Gaussian. 2021 May;10(2):259–68.

32. Ningrum HDP, Srinadi IGAM, Nilakusmawati DPE, Suciptawati NLP, Qur’ani AY, Jayanegara K. Modelling the Count of Diphtheria in West Java in 2022 using Geographically Weighted Zero-Inflated Poisson Regression. International Journal of Multidisciplinary Research and Growth Evaluation. 2024;5(5):378–84.

33. Karima N Al, Suyitno S, Hayati MN. Analisis Faktor-Faktor yang Mempengaruhi Jumlah Kasus Tuberkulosis di Indonesia Menggunakan Model Geographically Weighted Poisson Regression. EKSPONENSIAL. 2021 Jun 21;12(1):7.

34. Sintia I, Suyitno S, Hayati MN. Geographically Weighted Poisson Regression Model with Adaptive Bisquare Weighting Function (Case study: data on number of leprosy cases in Indonesia 2020). Jurnal Matematika, Statistika dan Komputasi. 2022 Sep 7;19(1):124–45.

35. Helmy H, Kamaluddin MT, Iskandar I, Suheryanto. Investigating Spatial Patterns of Pulmonary Tuberculosis and Main Related Factors in Bandar Lampung, Indonesia Using Geographically Weighted Poisson Regression. Trop Med Infect Dis. 2022 Aug 26;7(9):212.

36. Purnami SW, Qomariyah N, Purnomo S. Pemodelan Faktor-Faktor yang Memengaruhi Jumlah Kematian Ibu di Jatim dengan Pendekatan GWPR Ditinjau dari Segi Fasilitas Kesehatan. Jurnal Sains dan Seni ITS. 2013;2(2):311–6.

37. Sogen DL, Arum PR, Wasono R. Pemodelan Geographically Weighted Poisson Regression (GWPR) dengan Pembobot Fixed Bisquare Kernel dan Adaptive Bisquare Kernel pada Kasus DBD di Riau. In: Prosiding Seminar Nasional Unimus [Internet]. Semarang: Universitas Muhammadiyah Semarang; 2023 [cited 2025 Jul 19]. p. 371–87. Available from: https://prosiding.unimus.ac.id/index.php/semnas/article/view/1480

38. Arsyad S, Zainil Y. Research gap strategies in article introductions of different rank applied linguistics journals. Studies in English Language and Education. 2023 Jan 31;10(1):216–34.

39. Michael Nnaemeka Ajemba, Ebube Chinwe Arene. Research gaps for future research and their identification. World Journal of Advanced Research and Reviews. 2022 Oct 30;16(1):575–9.

40. Schober P, Vetter TR. Count Data in Medical Research: Poisson Regression and Negative Binomial Regression. Anesth Analg. 2021 May 14;132(5):1378–9.

41. Zhang K, Liu J, Liu Y, Zhang P, Carroll RJ. Bayesian adjustment for measurement error in an offset variable in a Poisson regression model. Stat Modelling. 2022 Dec 24;22(6):509–26.

42. Feng CX. A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. J Stat Distrib Appl. 2021 Dec 24;8(1):8.

43. Yu H, Fotheringham AS, Li Z, Oshan T, Wolf LJ. On the measurement of bias in geographically weighted regression models. Spat Stat. 2020 Aug;38:100453.

44. Chen TL, Lin ZH, Jheng DC. Spatial regression analysis of land use impact on land surface temperature in four East Asian metropolises. Sci Rep. 2025 Jul 1;15(1):22252.

45. Abelairas-Etxebarria P, Astorkiza I. From Exploratory Data Analysis to Exploratory Spatial Data Analysis. Mathematics and Statistics. 2020 Mar;8(2):82–6.

46. Naito M. Utilization and Application of Public Health Data in Descriptive Epidemiology. J Epidemiol. 2014;24(6):435–6.

47. Tyas SW, Gunardi, Puspitasari LA. Geographically weighted generalized poisson regression model with the best kernel function in the case of the number of postpartum maternal mortality in east java. MethodsX. 2023;10:102002.

48. Berliana SM, Purhadi, Sutikno, Rahayu SP. Parameter Estimation and Hypothesis Testing of Geographically Weighted Multivariate Generalized Poisson Regression. Mathematics. 2020 Sep 7;8(9):1523.

49. Al-Hasani G, Asaduzzaman M, Soliman AH. Geographically weighted Poisson regression models with different kernels: Application to road traffic accident data. Commun Stat Case Stud Data Anal Appl. 2021 Apr 3;7(2):166–81.

50. Koç T. Bandwidth Selection in Geographically Weighted Regression Models via Information Complexity Criteria. Journal of Mathematics. 2022 Jan 28;2022(1).

Downloads

Published

2026-04-30

How to Cite

Raihannabil, S. D., Halma, K., & Hutagalung, R. M. (2026). Spatial Modeling in Public Health: A Review of Geographically Weighted Poisson Regression (GWPR) Applications. STATMAT: Jurnal Statistika Dan Matematika, 8(1), 73–86. https://doi.org/10.32493/sm.v8i1.54205

Issue

Section

Articles

Similar Articles

You may also start an advanced similarity search for this article.